The heating load calculation for a passive solar house in Denver has two components that most calculations address separately: the envelope loss and the solar contribution. To design the passive solar system correctly, you need to understand both — and their relationship to each other over the course of a heating season.
The Envelope Loss Calculation
The envelope heat loss is calculated using the steady-state formula:
Q = U x A x (Ti - To)
Where:
- Q = heat loss rate (BTU/hour or Watts)
- U = overall heat transfer coefficient of the assembly (1/R-value)
- A = area of the assembly
- Ti = interior temperature (typically 20 C for design)
- To = outdoor design temperature (-18 C for Denver at 99 percent)
For a complete building, this calculation runs for every component: walls (by type and orientation), roof, floor (if over unconditioned space), windows, and doors. The sum is the total envelope loss at design conditions.
For a 280 square meter house in Denver with:
- Walls at effective R-30 (including thermal bridges): approximately 12 kW at design conditions
- Roof at effective R-50: approximately 4 kW
- Windows (triple pane at U-0.15): approximately 5 kW
- Floor over basement at R-15: approximately 2 kW
- Infiltration at 0.3 ACH in a tight envelope: approximately 3 kW
Total envelope loss at Denver design temperature: approximately 26 kW. This is the capacity the mechanical heating system must be able to deliver at the coldest design moment.
The Solar Gain Contribution
The passive solar gain through south-facing glazing on a clear winter day at Denver latitude is calculated as:
Solar gain = A x SHGC x Solar radiation x Transmission factor
Where:
- A = south-facing glazing area (square meters)
- SHGC = solar heat gain coefficient of the glass (typically 0.45 to 0.60 for passive solar south glass)
- Solar radiation = direct normal radiation at Denver latitude in January (approximately 4.5 to 5.5 kWh/m2/day on clear days)
- Transmission factor = shading coefficient from overhangs, frame, and interior obstructions (typically 0.85 to 0.95)
For 40 square meters of south-facing glazing at SHGC 0.50 and 4.5 kWh/m2/day of incident radiation:
Solar gain = 40 x 0.50 x 4.5 x 1000 Wh/day x 0.90 = 81,000 Wh/day = 81 kWh/day on a clear day
Daily heating load for the same house at Denver design temperature over 24 hours: 26 kW x 24 hours x 0.7 (average temperature differential over the day is typically 70 percent of the design differential) = approximately 437 kWh/day in extreme conditions.
The solar gain on a clear day (81 kWh) offsets about 19 percent of that extreme day load. But in typical January conditions — with average temperatures of -3 C rather than -18 C design temperature — the heating load is much lower and the solar fraction rises to 40 to 60 percent.
The Solar Fraction Over the Heating Season
Annual solar fraction is the useful metric: what fraction of the total heating energy for the season does passive solar provide?
At Denver, a well-designed passive solar house with:
- South glazing at 20 percent of floor area
- Thermal mass at the correct ratio to glazing area
- Effective envelope R-values in the R-25 to R-35 range
- Tight envelope at blower door testing
...typically achieves an annual solar fraction of 40 to 65 percent. This means 40 to 65 percent of the annual heating energy comes from the sun at no operating cost.
The remaining 35 to 60 percent is covered by mechanical heating — a system that is now sized at 40 to 65 percent less capacity than a non-solar house of the same size and envelope performance.
Glazing-to-Floor-Area Ratio as a Design Parameter
The glazing-to-floor-area (GFA) ratio for south-facing glass is the most directly controllable passive solar design variable. Too low and the solar fraction is limited by insufficient aperture. Too high and the thermal mass cannot absorb the peak solar gain, resulting in overheating on clear days.
The thermal mass requirement scales with the glazing area: approximately 6 to 8 square feet of 4-inch-thick concrete floor (or equivalent mass) per square foot of south-facing glazing. This is a floor area ratio that must be maintained for the system to work without overheating.
The matrix of options: we model three GFA ratios for most passive solar projects — conservative (15 percent of floor area), moderate (20 percent), and aggressive (25 percent) — and compare solar fraction, peak gain, thermal mass requirement, and capital cost for each. The client decides based on the comparison, not on a single recommended value.
Internal Gains: The Often-Ignored Contribution
In a well-insulated, tight house, internal gains — people, lighting, appliances, cooking — contribute meaningfully to the heating load balance. A family of four generates approximately 400 W of body heat continuously. Lighting and appliances in a typical house add 200 to 500 W during occupied hours.
These gains are not trivial against a 26 kW design heating load, but they are meaningful relative to the daily heating demand in mild January weather. Accounting for internal gains in the load calculation prevents over-sizing the mechanical backup system.
Próximos pasos
The passive solar heating load calculation sequence — envelope loss, solar gain by month, solar fraction, mechanical system sizing — is part of our design development deliverables for passive solar projects. The calculation drives the section geometry, not the other way around.